arXiv subjects

Faïcel Chamroukhi

Publications and source records attributed to Faïcel Chamroukhi.

4 recordsLinked to original sources

arXiv2026

Optimal Transport Aggregation for Distributed Mixture-of-Experts

Mixture-of-experts (MoE) models provide a flexible statistical framework for modeling heterogeneity and nonlinear relationships. In many modern applications, however, datasets are naturally distributed across multiple machines due to storage, computational, or governance constraints. We consider a distributed model aggregation setting in which local MoE models are trained independently on decentralized datasets and subsequently combined into a global estimator. Aggregating MoE models is challenging because standard averaging produces models that do not preserve the MoE structure, and therefore do not yield estimates of the global model parameters. To address this issue, we propose a principled aggregation framework based on optimal transport that constructs a reduced global MoE estimator by minimizing a transportation divergence between the collection of local estimators and the aggregated model. An efficient majorization--minimization (MM) algorithm is derived to solve the resulting optimization problem. The method requires only a single communication step from local machines to a central server, making it a frugal distributed learning approach particularly attractive for large-scale settings where communication costs are a major bottleneck. We further establish statistical guarantees for the aggregated estimator, including consistency under standard assumptions on the local estimators. Experiments on synthetic and real datasets demonstrate that the approach achieves performance comparable to centralized training while significantly reducing computation time. The source codes are publicly available on Github.

cs.LG↗

arXiv2025

Federated Dynamic Modeling and Learning for Spatiotemporal Data Forecasting

This paper presents an advanced Federated Learning (FL) framework for forecasting complex spatiotemporal data, improving upon recent state-of-the-art models. In the proposed approach, the original Gated Recurrent Unit (GRU) module within previous Dynamic Spatial--Temporal Graph Convolutional Recurrent Network (DSTGCRN) modeling is first replaced with a Long Short-Term Memory (LSTM) network, enabling the resulting model to more effectively capture long-term dependencies inherent to time series data. The resulting architecture significantly improves the model's capacity to handle complex temporal patterns in diverse forecasting applications. Furthermore, the proposed FL framework integrates a novel Client-Side Validation (CSV) mechanism, introducing a critical validation step at the client level before incorporating aggregated parameters from the central server into local models, ensuring only the most effective updates are retained and improving both the robustness and accuracy of the forecasting model across clients. The efficiency of our approach is demonstrated through extensive experiments on real-world applications, including public datasets for multimodal transport demand forecasting and private datasets for Origin-Destination (OD) matrix forecasting in urban areas. The results demonstrate substantial improvements over conventional methods, highlighting the framework's ability to capture complex spatiotemporal dependencies while preserving data privacy. This work not only provides a scalable and privacy-preserving solution for real-time, region-specific forecasting and management but also underscores the potential of leveraging distributed data sources in a FL context. We provide our algorithms as open-source on GitHub

cs.LG↗

arXiv2023

Functional Mixtures-of-Experts

We consider the statistical analysis of heterogeneous data for prediction in situations where the observations include functions, typically time series. We extend the modeling with Mixtures-of-Experts (ME), as a framework of choice in modeling heterogeneity in data for prediction with vectorial observations, to this functional data analysis context. We first present a new family of ME models, named functional ME (FME) in which the predictors are potentially noisy observations, from entire functions. Furthermore, the data generating process of the predictor and the real response, is governed by a hidden discrete variable representing an unknown partition. Second, by imposing sparsity on derivatives of the underlying functional parameters via Lasso-like regularizations, we provide sparse and interpretable functional representations of the FME models called iFME. We develop dedicated expectation--maximization algorithms for Lasso-like (EM-Lasso) regularized maximum-likelihood parameter estimation strategies to fit the models. The proposed models and algorithms are studied in simulated scenarios and in applications to two real data sets, and the obtained results demonstrate their performance in accurately capturing complex nonlinear relationships and in clustering the heterogeneous regression data.

stat.ME↗

arXiv2023

Data-driven Reachability using Christoffel Functions and Conformal Prediction

An important mathematical tool in the analysis of dynamical systems is the approximation of the reach set, i.e., the set of states reachable after a given time from a given initial state. This set is difficult to compute for complex systems even if the system dynamics are known and given by a system of ordinary differential equations with known coefficients. In practice, parameters are often unknown and mathematical models difficult to obtain. Data-based approaches are promised to avoid these difficulties by estimating the reach set based on a sample of states. If a model is available, this training set can be obtained through numerical simulation. In the absence of a model, real-life observations can be used instead. A recently proposed approach for data-based reach set approximation uses Christoffel functions to approximate the reach set. Under certain assumptions, the approximation is guaranteed to converge to the true solution. In this paper, we improve upon these results by notably improving the sample efficiency and relaxing some of the assumptions by exploiting statistical guarantees from conformal prediction with training and calibration sets. In addition, we exploit an incremental way to compute the Christoffel function to avoid the calibration set while maintaining the statistical convergence guarantees. Furthermore, our approach is robust to outliers in the training and calibration set.

cs.LG↗